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Calculus and Optimization for Machine Learning
Week 5
Practice Quiz #2

Practice QuizPractice Quiz • 30 min30 minutes

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Practice Quiz #2

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Practice Quiz #2

Total points 4

1.

Question 1

Assume that two function $f(x)$ and $g(x)$ diverge only in one point on the segment $[a, b]$ . According to the limit definition of the definite integral, do the areas under this two curve over $[a,b]$ coincide?

1 / 1 point

Depends on the tagging

Yes

Depends on the differences in the point of divergence

No

Correct

Correct!

2.

Question 2

Choose correct statements (there could be more than one; all entities in question are supposed to exist):

1 / 1 point

$\int_a^b f(x)dx+\int_b^c f(x)dx=\int_a^c f(x)dx$

Correct

Correct! Quite obvious if you think in terms of areas.

$\int_a^a f(x)dx=0$

Correct

Yes, we are talking about the area of the segment!

$\int_a^b f(x)dx=-\int_b^a f(x)dx$

Correct

Weird but corresponds to the two previous threads!

3.

Question 3

Find $\int_0^{\pi/2} \sin^2 x dx$ .

1 / 1 point

\frac{\pi}{4}

pi/4

Correct

4.

Question 4

Find $\int_0^1 \ln x dx$ .

1 / 1 point

-1

-1

Correct

Correct!